Rapid filtration methods for dual-energy x-ray ct

ABSTRACT

Systems and method for performing X-ray computed tomography (CT) that can improve spectral separation and decrease motion artifacts without increasing radiation dose are provided. The systems and method can be used with either a kVp-switching source or a single-kVp source. When used with a kVp-switching source, an absorption grating and a filter grating can be disposed between the X-ray source and the sample to be imaged. Relative motion of the filter and absorption gratings can by synchronized to the kVp switching frequency of the X-ray source. When used with a single-kVp source, a combination of absorption and filter gratings can be used and can be driven in an oscillation movement that is optimized for a single-kVp X-ray source. With a single-kVp source, the absorption grating can also be omitted and the filter grating can remain stationary.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional PatentApplication Ser. No. 62/319,881, filed Apr. 8, 2016, and U.S.Provisional Patent Application Ser. No. 62/333,882, filed May 10, 2016,the disclosures of which are hereby incorporated by reference in theirentirety, including any figures, tables, and drawings.

BACKGROUND

Since the invention of X-ray computed tomography (CT) in 1971, it hasgone through many improvements, including fanbeam, multi-slice andcone-beam spiral CT methods, which add longitudinal dimension to CTimages. Also, dual-energy/multi-energy CT technologies add spectraldimension to CT images. Even though dual-energy CT has some advantages,monochromatic imaging and material decomposition can be performed, whichreduces X-ray radiation dose and facilitates a number of importantapplications. Multi-energy CT is an emerging field, but it still needstime to become mature and enter the clinical world.

Currently, dual-energy CT technologies can be classified into threecategories: kVp-switching; dual-layer detection; and dual-sourcescanning. The kVp-switching method is an X-ray source technology inwhich low- and high-energy X-ray beams are alternatingly emitted duringa scan. The dual-layer detector method is based on a detector innovationso that low- and high-energy data are collected in two sensor layersrespectively. These two methods both use a single X-ray source togenerate dual-energy datasets. Thus, the resultant low- and high-energydatasets share the same X-ray filter placed in front of the X-raysource. Different from the single-source-based dual-energy CT systems, adual-source system includes two imaging subsystems. The dual-source CTsystem is more expensive, and there is a temporal discrepancy betweenlow- and high-energy data acquisitions. Breathing, heart beating, andpatient motion causes artifacts in reconstructed images, compromisingmaterial decomposition and monochromatic imaging.

BRIEF SUMMARY

Embodiments of the subject invention include systems and method forperforming X-ray computed tomography (CT) that can improve spectralseparation and decrease motion artifacts without increasing radiationdose to which a patient is exposed during imaging. Systems and methodsof embodiments of the subject invention can be used with either akVp-switching source or a single-kVp source. When used with akVp-switching source, an absorption grating and a filter grating can bedisposed between the X-ray source and where a sample/patient to beimaged would be (or is) located (e.g., in front of the X-ray source).Relative motion of the filter and absorption gratings can bysynchronized to the kVp switching frequency of the X-ray source.Different filter regions can be exposed to X-rays at various timeinstants, thereby producing low- and high-energy X-rays accordingly.When used with a single-kVp source, a combination of absorption andfilter gratings can be used and can be driven in an oscillation movementthat is optimized for a single-kVp X-ray source. In certain embodiments,only a filter grating alone is required, and the filter grating can bestationary with respect to the X-ray source. In a specific embodiment,the filter grating can be just a two-strip filter.

In an embodiment, a system for performing X-ray CT imaging can comprise:an X-ray source; a detector for detecting X-ray radiation from thesource; a filter grating disposed between the source and the detector;and an absorption grating disposed between the filter grating and thesource. At least one of the absorption grating and the filter gratingcan be configured to move relative to the other during operation of thesource. The filter grating can be positioned closer to the source thanit is to the detector (for example, in front of the source). The sourcecan be either a kVp-switching source or a non-kVp-switching source, andthe oscillation (relative movement) between the gratings can beoptimized depending on what type of source is used.

In another embodiment, a system for performing X-ray CT imaging cancomprise: a single-kVp X-ray source (non-kVp-switching X-ray source); adetector for detecting X-ray radiation from the source; and a filtergrating disposed between the source and the detector. The filter gratingcan be positioned closer to the source than it is to the detector (forexample, in front of the source, and the system can specifically excludean absorption grating. The filter grating can be configured to bestationary during operation of the source. Image reconstruction for sucha system can be based on a non-linear X-ray data generation model. Theimage reconstruction can include non-linear data modeling and compressedsensing.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1A shows a depiction of kVp-switching X-ray computed tomography(CT).

FIG. 1B shows a depiction of dual-layer detection X-ray CT.

FIG. 1C shows a depiction of dual-source scanning X-ray CT.

FIG. 1D shows a plot of low- and high-energy spectra for kVp-switchingX-ray CT.

FIG. 1E shows a plot of low- and high-energy spectra for dual-layerdetection X-ray CT.

FIG. 1F shows a plot of low- and high-energy spectra for dual-sourcescanning X-ray CT.

FIG. 2A shows example filter and absorption gratings that can be used ina system or method according to an embodiment of the subject invention.

FIG. 2B shows a layout of gratings disposed in front of an X-ray sourceaccording to an embodiment of the subject invention.

FIG. 2C shows a stationary curved absorption grating that can be usedaccording to an embodiment of the subject invention.

FIG. 2D shows a top view of a grating having slits designed for a curvedgeometry according to an embodiment of the subject invention.

FIG. 3A shows an oscillation curve of a filter grating.

FIG. 3B shows a top view of an absorption grating (left) and a filtergrating (right) including two different types of filter (differentshadings) according to an embodiment of the subject invention.

FIG. 3C shows a top view of an absorption grating (left) and a filtergrating (right) including two different types of filter (differentshadings) according to an embodiment of the subject invention.

FIG. 3D shows a top view of an absorption grating (left) and a filtergrating (right) including two different types of filter (differentshadings) according to an embodiment of the subject invention.

FIG. 4A shows the exposure window for two different types of filters ofthe same filter grating at a duty cycle of 30%, with the vibrationamplitude being half of the filter grating period, according to anembodiment of the subject invention.

FIG. 4A shows the exposure window for two different types of filters ofthe same filter grating at a duty cycle of 50%, with the vibrationamplitude being half of the filter grating period, according to anembodiment of the subject invention.

FIG. 4C shows a plot of effective filtration area as a function ofabsorption grating duty cycle (r).

FIG. 5A shows a plot of spectral distributions at an absorption gratingduty cycles of 70%.

FIG. 5B shows a plot of spectral distributions at an absorption gratingduty cycles of 50%.

FIG. 5C shows a plot of spectral distributions at an absorption gratingduty cycles of 30%.

FIG. 6A shows a top schematic view of a setup according to an embodimentof the subject invention.

FIG. 6B shows a top schematic view of a setup according to an embodimentof the subject invention.

FIG. 6C shows a top schematic view of a setup according to an embodimentof the subject invention.

FIG. 6D shows a collected CT sinogram.

FIG. 6E shows an image of collected data for a CT scan.

FIG. 7A shows a plot of spectral distributions for a two-strip grating.

FIG. 7B shows a plot of spectral distributions for a multi-stripgrating.

FIG. 8 shows a chest phantom.

FIG. 9 shows eight reconstructed monochromatic images from a numericalsimulation of CT scans.

FIG. 10 shows eight enlarged images of the local metal areas (the areasaround the rods represented by the dots near the lower-middle section ofthe phantom) of the corresponding images from FIG. 9.

FIG. 11 shows eight reconstructed monochromatic images from a numericalsimulation of CT scans.

FIG. 12 shows eight enlarged images of the local metal areas (the areasaround the rods represented by the dots near the lower-middle section ofthe phantom) of the corresponding images from FIG. 11.

FIG. 13A shows a plot of signal-to-noise ratio (SNR) for the images ofFIG. 9.

FIG. 13B shows a plot of SNR for the images of FIG. 11.

FIG. 14 shows nine reconstructed monochromatic images from a numericalsimulation of CT scans.

FIG. 15 shows a plot of SNR versus energy for the images of FIG. 14.

FIG. 16 shows reconstructed monochromatic images from a numericalsimulation of CT scans.

FIG. 17 shows reconstructed monochromatic images from a numericalsimulation of CT scans (top portion) and a plot of SNR versus number ofprojections.

FIG. 18 shows four plots for K-edge filtering, with two plots ofnormalized spectra versus X-ray energy (top portion) and two plots ofspectra versus X-ray energy (lower portion).

DETAILED DESCRIPTION

Embodiments of the subject invention include systems and method forperforming X-ray computed tomography (CT) that can improve spectralseparation and decrease motion artifacts without increasing radiationdose to which a patient (e.g., a mammal patient such as a human) orsample is exposed during imaging. Systems and methods of embodiments ofthe subject invention can be used with either a kVp-switching(kilovolt-peak-switching (voltage-alternating)) X-ray source or asingle-kVp (non-kVp-switching) X-ray source (e.g., X-ray tube). Whenused with a kVp-switching X-ray source, an absorption grating and afilter grating can be disposed between the X-ray source and where asample/patient to be imaged would be (or is) located (e.g., in front ofthe X-ray source). Relative motion of the filter and absorption gratingscan by synchronized to the kVp switching frequency of the X-ray source(e.g., X-ray tube). Different filter regions can be exposed to X-rays atvarious time instants, thereby producing low- and high-energy X-raysaccordingly. When used with a single-kVp (non-kVp-switching) X-raysource, a combination of absorption and filter gratings can be used andcan be driven in an oscillation movement (relative to each other) thatis optimized for a single-kVp X-ray source. With X-rays of the sameenergy spectrum, different filtration materials can be used to generateX-rays in two (or more) energy spectra (one of them at any given timeinstant). In certain embodiments, only a filter grating alone isrequired, and the filter grating can be stationary with respect to theX-ray source (e.g., X-ray tube). This stationary approach presents aminimum demand for CT hardware enhancement. In a specific embodiment,the filter grating can be just a two-strip filter.

Dual-energy CT technologies can be classified into the three categories:kVp-switching; dual-layer detection; and dual-source scanning. FIGS.1A-1C are depictions of beams for kVp-switching, dual-layer detection,and dual-source scanning, respectively. The kVp-switching method is anX-ray source technology in which low- and high-energy x-ray beams arealternatingly emitted during a scan. The dual-layer detector method isbased on a detector innovation so that low- and high-energy data arecollected in two sensor layers respectively. These two methods both usea single X-ray source to generate dual-energy datasets. Generally, theresultant low- and high-energy datasets share the same X-ray filterplaced in front of the X-ray source, and as a result, the low- andhigh-energy X-rays are not well separated, as shown in FIGS. 1D and 1E,which are plots for conventional kVp-switching and dual-layer detection,respectively, of low- and high-energy spectra. In a dual-source system,there are two imaging subsystems. Because the X-ray sources areindependent, different X-ray filters can be customized for more flexibleX-ray filtration, and the low- and high energy X-ray entrance spectracan be individually shaped, yielding a better spectral separation, asshown in FIG. 1F. However, dual-source CT systems are more expensive andresult in a temporal discrepancy between low- and high-energy dataacquisitions. Breathing, heart beating, and patient motion causeartifacts in reconstructed images for related art dual-source systems,compromising material decomposition and monochromatic imaging.

Embodiments of the subject invention can simultaneously address thespectral overlapping problem with kVp-switching and dual-layer detectionsystems, as well as the motion artifact problem with a dual-sourcescanner. Grating oriented line-wise filtration (GOLF) systems andmethods can enable interlaced filtration patterns for superior energyseparation. An X-ray filtration device can be easily integrated into aCT scanner and its scanning procedure. Depending on the X-ray sourcetype, three main filtration systems/methods can be used, which can bereferred to as GOLF_(k), GOLF_(c), and GOLF_(s).

GOLF_(k) can be used for a kVp-switching X-ray source. GOLF_(k) cancombine an absorption grating and a filter grating disposed between theX-ray source and where a sample/patient to be imaged would be (or is)located (e.g., in front of the X-ray source). GOLF_(k) can synchronizerelative motion of the filter and absorption gratings to the kVpswitching frequency of the X-ray source (e.g., X-ray tube). For example,the filter grating can be driven by a high-precision manipulator, suchas a piezo-electrical motor for rapid oscillation of one gratingrelative to the other. Different filter regions can be exposed to X-raysat various time instants, thereby producing low- and high-energy X-raysaccordingly.

GOLF_(c) and GOLF_(s) can work with a conventional (e.g.,non-kVp-switching) X-ray source. GOLF_(c) can use a combination ofabsorption and filter gratings optimized for an X-ray source (e.g.,X-ray tube) without kVp-switching. The X-ray filter grating and/or theX-ray absorption grating can be driven in an oscillation movementrelative to each other. GOLF_(s) only requires a filter grating alonethat is stationary with respect to the X-ray source (e.g., X-ray tube).This stationary approach presents a minimum demand for CT hardwareenhancement. In a specific embodiment of GOLF_(s), the filter gratingcan be just a two-strip filter.

FIG. 2A shows example filter and absorption gratings that can be used ina GOLFk system or method according to an embodiment of the subjectinvention, and FIG. 2B shows a layout of gratings disposed in front ofthe X-ray source. Although FIG. 2A shows an X-ray tube with electronbeam and anode as the X-ray source, along with two filters making up thefilter grating, these are for exemplary purposes only and should not beconstrued as limiting. Referring to FIGS. 2A and 2B, the absorptiongrating can be disposed between the X-ray source and the filter grating,and the gratings can be moved relative to each other during operation ofthe X-ray source. The movement of the gratings can be in a directionparallel to the front face of the grating (i.e., in the z-direction asdepicted in FIG. 2B). In addition, the filter grating can include onefilter or a plurality of filters. The absorption grating can comprise orbe entirely composed of an X-ray absorption material (e.g., gold) to letX-rays go through its open slits only. In this way, the X-rays allowedto go through can be controlled by choosing the width of each slit, thenumber of slits, the width between slits, and the number of solidportions (non-slits). The width of slits and/or solid portions can beuniform across the grating, individually or in total, or such widths canvary. The filter grating can spectrally modify the X-ray beam throughgrating materials. For example, the filter grating can include thinmetal strips interlacing one or more filtering materials (e.g., twofiltering materials). The duty cycle of the filter grating can be, forexample, 50%, though embodiments are not limited thereto. Throughrelative displacement of the two gratings, incident X-rays are filteredat different time instants by different kinds of filtering strips. Also,in further embodiments, a plurality of absorption gratings and/or filtergratings can be used.

The two gratings can be overlaid in front of the X-ray source, as shownin FIG. 2B. In the kVp-switching based dual-energy CT system, theentrance X-rays can alternate at low- and high-energy levels.Synchronously, the filter grating can be driven at the samehigh-frequency relative to the absorption grating. For low-energy X-rayimaging, the filter grating can oscillate in such a way that the firstset of filtering strips happen to be in the X-ray path. Then, forhigh-energy X-ray imaging, the second set of filtering strips can beexposed to the X-ray source.

In certain embodiments, the gratings can be configured to fit a curvedgeometry. FIG. 2C shows a stationary curved absorption grating, and FIG.2D shows a top view of a grating having slits designed for a curvedgeometry. Referring to FIGS. 2C and 2D, one or more gratings can beconfigured to fit a curved geometry, such as for a third generation CTimplementation. The strips in a curved absorption grating can be alignedaccording to X-ray emitting angles in a cone geometry, as shown in FIG.2C. In a specific embodiment, the period of the filter grating can be0.5 mm with a duty cycle of 50%, the strips in the flat absorptiongrating can be made of 1 mm gold strips with high X-ray absorption, andthe materials of the filter grating are air and 1 mm tin correspondingto low- and high-energy X-ray filtrations, respectively.

In embodiments of a GOLFk system or method, the motion direction of thefilter grating can be perpendicular to the longitudinal direction of thefilter strips. Thus, half (or about half) of the original X-rays can beblocked by the absorption grating, and the other half (or about half)can get filtered by the corresponding strips of the filter grating. WithkVp-switching based dual-energy CT, the low- and high-energy X-rays areemitted in turn.

In many embodiments of a GOLFk system or method, the filter gratingvibration frequency can be matched to the X-ray kVp-switching frequency.Also, the vibration amplitude can be optimized according to the dutycycle of the absorption grating. With the duty cycle being ½r, theoptimized vibration amplitude is

$\left( {1 - r} \right){\frac{p}{2}.}$

FIG. 3A snows an oscillation curve of a filter grating according to anembodiment. Referring to FIG. 3A, the oscillation period is equal tohalf the time interval between two adjacent X-ray projections in thekVp-switching CT scan. FIGS. 3B-3D show top views of an absorptiongrating (left) and a filter grating (right) including two differenttypes of filter (different shadings). An ideal X-ray filtration settingis shown in FIG. 3C, in which the absorption grating and the filtergrating are in a perfect alignment, without filter materials mixed inthe x-ray beam. Referring to FIG. 3C, the filter grating can be alignedsuch that one of its filter materials matches up with each slit of theabsorption grating. However, during the exposure period t, theabsorption grating and the filter grating are in relative motion, andthe X-rays are filtered by two filters with a changing material mixture,for example leading to the orientation shown in FIG. 3B at certaintimes. FIG. 3D shows an example absorption grating with a narrowergrating opening. Referring to FIG. 3D, the configuration with a narroweropening minimizes the problems that may be caused by mixed filtration,but this can come at a cost of reduced photon efficiency.

FIGS. 4A-4B show the exposure window for two different types of filtersof the same filter grating at duty cycles of 30% and 50%, respectively,for the vibration amplitude being half of the filter grating period.FIG. 4C shows a plot of effective filtration area as a function ofabsorption grating duty cycle (r). FIGS. 4A-4C are all for a GOLF_(k)system/method according to an embodiment of the subject invention.Referring to FIGS. 4A and 4B, within the exposure window Δt, Filters 1and 2 are gradually exposed through the absorption grating opening, inwhich Filter 1 offers the correct filtration, while Filter 2 introducesa contamination. Referring to FIG. 4C, by increasing the open ratio to1, the filtration method is degraded to the conventional kVp-switchingmethod.

FIGS. 5A-5C show plots of spectral distributions for a GOLF_(k)system/method according to an embodiment of the subject invention, atabsorption grating duty cycles of 70%, 50%, and 30%, respectively. InFIGS. 5A-5C, vertical dotted lines indicate corresponding mean energies(also labeled on the plots), and in each of these plots, the left-mostplotted line is for an energy of 80 kVp and the right-most plotted lineis for an energy of 140 kVp. The plots in FIGS. 5A-5C assume air and 1mm tin as two filtering materials in the filter grating. Referring toFIGS. 5A-5C, a narrower absorption grating opening results in betterseparation of the spectra; though, a narrow absorption grating openingcan decrease the X-ray efficiency.

GOLF_(c) and GOLF_(s) systems and methods as described herein can beused with an X-ray source with no kVp-switching (and, optionally,without any other advanced features). FIGS. 6A-6C show top schematicviews of a GOLF_(c) setup according to various embodiments of thesubject invention. The X-ray sources shown in FIGS. 6A-6C are forexemplary purposes only and should not be construed as limiting. In anembodiment, a degraded grating filter can include only two filterstrips, one of which is low-absorption material (e.g., air or aluminum)and the other is a high-absorption material (e.g., tin). Thelow-absorption material can keep the original X-ray beam while thehigh-absorption material can harden the X-ray beam (see also FIGS.6A-6C). With this GOLF_(c) setup, two mean-energy parts can be formed inone full X-ray beam. FIG. 6D shows the collected CT sinogram, in whichthe left side is low mean-energy data, and the other side highmean-energy data, which are for low-energy and high-energy imagereconstruction, respectively. Given the size of the X-ray focal spot, apenumbra can be seen along the middle line of the sinogram, as marked bythe (red) arrow in FIG. 6D, which will influence the imagereconstruction. To address this effect, relative displacement betweenthe X-ray focal spot and filter grating can be introduced. It can beimplemented, for example, via e-beam control in the X-ray tube (theflying focal spot method) or filter oscillation outside the X-raysource; these two methods are equivalent in principle.

In a specific embodiment of GOLF_(c), the low- and high-absorptionmaterials can be 0.1-mm and 1.0-mm tin materials, respectively, and thesize of the X-ray focal spot can be 1 mm. In this case, the penumbra inthe detector plane is about 8 mm in width under the imaging geometry ofa system in which the filter is 10 cm away from the X-ray focal spot. Bycontrolling the X-ray focal spot flying in 1 mm along the X-axis oroscillating the filter with 1 mm peak shift, the collected data areshown in FIG. 6E, which can remove the penumbra effect although theamount of effective central data are reduced by half. As a result, themiddle strip in FIG. 6D can become usable after longitudinal datainterpolation for dual-energy image reconstruction via filtered backprojection (see, e.g., references [20] and [21] in the Referencessection, both of which are hereby incorporated herein by reference intheir entireties).

FIGS. 7A and 7B show plots of spectral distribution for a GOLF_(c) setupfor a two-strip grating and a multi-strip (more than two-strip) grating,respectively, according to an embodiment of the subject invention. Toobtain the plots in FIGS. 7A and 7B, the two types of filteringmaterials were 0-mm titanium (air) and 1.0-mm titanium materials. InFIGS. 7A and 7B, vertical dotted lines indicate corresponding meanenergies (also labeled on the plots), and in each of these plots, theright-most plotted line is for 1.0 mm tin (50% duty cycle in FIG. 7B).In FIG. 7A, the left-most plotted line is for 0.1 mm tin, and in FIG.7B, the left-most plotted line is for 0.0 mm tin at 50% duty cycle. Moregenerally, in GOLF_(c) the two-strip filter can be replaced by a gratingcomprising alternating strips, coupled with an absorption grating asdescribed with reference to GOLF_(k). With this grating method, therelative displacement between the X-ray focal spot and the filtergrating is not needed because the motion of the absorption gratingdefines the filtration for the X-ray beam. However, the drawback of thegrating method is its low X-ray flux efficiency. FIG. 7B is based on amulti-strip grating including 0-mm titanium (air) and 1.0-mm titaniummaterials with a duty cycle of 50%.

The GOLF_(c) systems and methods described herein can be used with aconventional X-ray source that does not include kVp-switching, therebyrelaxing the need for a kVp-switching X-ray source. However, dynamicrelative grating displacement can still be used to select X-rayfiltration effects. The dual-energy imaging system can be furthersimplified with a stationary filtering grating alone or just astationary two-strip filter where an X-ray imaging model is necessary toseparate mixed spectra for hybrid imaging reconstruction (see also,e.g., reference [22] in the References section, which is herebyincorporated herein by reference in its entirety). The stationaryfiltering grating methods can be referred to as “GOLF_(s)”.

A monochromatic image can be reconstructed in both the projection andimage domains (see, e.g., references [8] and [23] in the Referencessection, both of which are hereby incorporated herein by reference intheir entireties). This is based on the assumption that any material canbe represented as a linear combination of two basis materials:

$\begin{matrix}{{\mu^{t} = {{\left( \frac{\mu}{\rho} \right)_{1}^{t}\rho_{1}} + {\left( \frac{\mu}{\rho} \right)_{2}^{t}\rho_{2}}}},{i = L},H} & (1)\end{matrix}$

where “L” and “H” indicate low- and high-energy, respectively, and “1”and “2” indicate the two basis materials, respectively. Mass densities(p₁, p₂) of the two basis materials are used to characterize anymaterial. In the projection domain (p) and image domain (p), there arelow- and high-energy datasets and images (p^(L), p^(H) and μ^(L),μ^(H)). The monochromatic image CT(E) at any x-ray energy E can bereconstructed from projections.

P(E)=w(E)·P ^(L)+(1−w(E))·P ^(H).  (2)

Specifically,

CT(E)=recon(P(E))  (3)

and

CT(E)=w(E)·CT ^(L)+(1−w(e))·CT ^(H),  (4)

where the weighting factor is

$\begin{matrix}{{w(E)} = {\frac{{{\mu_{1}(E)} \cdot \mu_{2}^{H}} - {{\mu_{2}(E)} \cdot \mu_{1}^{H}}}{{\mu_{1}^{L} \cdot \mu_{2}^{H}} - {\mu_{1}^{H} \cdot \mu_{2}^{L}}} \cdot {\frac{\mu_{2}^{L}}{\mu_{2}(E)}.}}} & (5)\end{matrix}$

Systems and method of embodiments of the subject invention, incombination with single-kVp imaging and kVp-switching technology, opennew doors to extract dual energy data effectively, with flexibility, andimproved cost-effectiveness. The key feature of dual-energy CT imagingis the spectral separation that helps avoid spectral mixing and revealsmore information regarding material composition and monochromaticimaging. Systems and method of embodiments of the subject invention cantake advantage of these attributes of dual-energy CT imaging while alsoaddressing the motion artifact problem with a dual-source scanner andthe spectral overlapping problem with kVp-switching and dual-layerdetection systems.

Three main types of GOLF systems and method have been described,including GOLF_(k), GOLF_(c), and GOLF_(s). GOLF_(k) performs the bestin terms of spectral separation, and a combination of absorptiongrating(s) and filter grating(s) can be used with a single-source CTsystem to achieve dual-source, dual-energy CT performance similar tothat in a GOLF_(c) system/method. When a kVp-switching X-ray sourcecannot be used, a GOLF_(c) or GOLF_(s) system/method can be used tosignificantly improve spectral separation. GOLF_(s) can be thought of asthe simplest case of GOLF_(c) with the highest photon utilization.GOLF_(s) can work in a stationary mode with only one filter grating, forexample in a full scan. The image reconstruction algorithm for GOLF_(s)can be based on a non-linear X-ray data generation model.

Embodiments of the subject invention can include dynamically modulatingthe filter grating of millimeter-/sub-millimeter-sized filtering stripsby a matching absorption grating with a small oscillation amplitude at ahigh frequency. Due to this micro-technology, the medical CTrequirements for full coverage over the field of view and a rapid changein filtration settings can be simultaneously achieved to yield superiorspectral filtration. The filter vibration can be driven by, for example,a piezo-electrical device, which is a mature technology compatible withCT scanning. The use of an absorption grating does result in the loss ofsome X-ray flux from the source. The duty cycle of the absorptiongrating can balance the X-ray spectral separation and the X-ray fluxutilization. If the duty cycle of the absorption grating is 100%(r=100%), the system is equivalent to a conventional kVp-switching baseddual-energy CT; while as r gets closer to 0, spectral separation gain isincreased while more X-rays are blocked (X-ray flux decreases). Betterspectral separation (narrower opening slits) leads to better quality ofreconstructed monochromatic images without having to increase theradiation dose to which the patient (e.g., a mammal such as a human) orsubject is exposed during imaging.

In GOLF_(s) systems and methods according to embodiments of the subjectinvention, a filter grating can be used with no absorption grating,thereby not completely blocking the path of any X-rays. The imagereconstruction from data collected with GOLF_(s) can be morecomplicated, involving non-linear data modeling and compressed sensing(see also reference [22] from the References section, which is herebyincorporated herein by reference in its entirety). Spectral mixing inmultiple penumbras could be an issue.

It is emphasized that in addition to the explicitly described designs,many variations are possible in the spirit of the invention. Forexample, the gratings can be made in 2D instead of 1D (e.g., to fit intocone-beam geometry). Also, more than two filtering material types can beintroduced (e.g., for multi-energy x-ray imaging). Also, X-ray pathlengths in the patient body can be taken into account so that the finaldiagnostic performance can be optimized instead of the spectralseparation itself, which is an indirect measure anyway.

Embodiments of the subject invention can advantageously be used withexisting X-ray CT systems with minimal overhead expense. The imagingperformance can be improved significantly in terms of monochromaticimage quality, material decomposition, and radiation dose reduction.Although the use of an absorption grating can decrease the efficiency ofthe X-ray source, patient radiation dose is not increased, so this isnot a major drawback.

The methods and processes described herein can be embodied as codeand/or data. The software code and data described herein can be storedon one or more machine-readable media (e.g., computer-readable media),which may include any device or medium that can store code and/or datafor use by a computer system. When a computer system and/or processerreads and executes the code and/or data stored on a computer-readablemedium, the computer system and/or processer performs the methods andprocesses embodied as data structures and code stored within thecomputer-readable storage medium.

It should be appreciated by those skilled in the art thatcomputer-readable media include removable and non-removablestructures/devices that can be used for storage of information, such ascomputer-readable instructions, data structures, program modules, andother data used by a computing system/environment. A computer-readablemedium includes, but is not limited to, volatile memory such as randomaccess memories (RAM, DRAM, SRAM); and non-volatile memory such as flashmemory, various read-only-memories (ROM, PROM, EPROM, EEPROM), magneticand ferromagnetic/ferroelectric memories (MRAM, FeRAM), and magnetic andoptical storage devices (hard drives, magnetic tape, CDs, DVDs); networkdevices; or other media now known or later developed that is capable ofstoring computer-readable information/data. Computer-readable mediashould not be construed or interpreted to include any propagatingsignals. A computer-readable medium of the subject invention can be, forexample, a compact disc (CD), digital video disc (DVD), flash memorydevice, volatile memory, or a hard disk drive (HDD), such as an externalHDD or the HDD of a computing device, though embodiments are not limitedthereto. A computing device can be, for example, a laptop computer,desktop computer, server, cell phone, or tablet, though embodiments arenot limited thereto.

The subject invention includes, but is not limited to, the followingexemplified embodiments.

Embodiment 1. A system for performing X-ray computed tomography (CT)imaging, the system comprising:

an X-ray source;

a detector for detecting X-ray radiation from the source;

a filter grating disposed between the source and the detector (to modifythe original X-ray energy spectrum of the X-ray radiation of the X-raysource into two or more spectra), wherein the filter grating ispositioned closer to the source than the detector is; and

an absorption grating aligned with the filter grating (either before thefilter grating or after the filter grating, along a path of X-rayradiation from the source to the detector) (to selectively block atleast a portion of the X-ray radiation from reaching the filter gratingso that a preferred X-ray spectrum can pass through the filter gratingand can go through a patient or subject to be imaged at a given timeinstant),

wherein at least one of the absorption grating and the filter grating isconfigured to move relative to the other during operation of the source.

Embodiment 2. The system according to embodiment 1, wherein the sourceis a kVp-switching X-ray source.

Embodiment 3. The system according to embodiment 2, wherein theabsorption grating and the filter grating oscillate relative oneanother, and the oscillation is synchronized with a switching frequencyof the source, such that each time the source switches its voltagelevel, at least one of the absorption grating and the filter gratingmoves relative to the other.

Embodiment 4. The system according to any of embodiments 2-3, wherein anoscillation period of the relative movement between the gratings isequal to half a time interval between two adjacent X-ray projections ofthe source.

Embodiment 5. The system according to embodiment 1, wherein the sourceis a single-kVp X-ray source (non-kVp-switching X-ray source).

Embodiment 6. The system according to embodiment 5, wherein the relativemovement of the gratings is an oscillation movement (relative to eachother) that is optimized for the single-kVp X-ray source.

Embodiment 7. The system according to any of embodiments 1-6, whereinthe filter grating comprises at least two different types of filtermaterial.

Embodiment 8. The system according to any of embodiments 1-7, whereinthe filter grating comprises exactly two different types of filtermaterial.

Embodiment 9. The system according to any of embodiments 1-8, whereinthe absorption grating comprises slit portions and solid portionsdisposed alternatingly.

Embodiment 10. The system according to embodiment 9, wherein a width ofeach slit portion of the absorption grating is the same as that of eachother slit portion of the absorption grating.

Embodiment 11. The system according to any of embodiments 9-10, whereina width of each solid portion of the absorption grating is the same asthat of each other solid portion of the absorption grating.

Embodiment 12. The system according to any of embodiments 9-11, whereina width of each slit portion of the absorption grating is the same asthat of each solid portion of the absorption grating.

Embodiment 13. The system according to any of embodiments 9-11, whereina width of at least one slit portion of the absorption grating isdifferent from that of at least one solid portion of the absorptiongrating.

Embodiment 14. The system according to any of embodiments 9-11, whereina width of at least one slit portion of the absorption grating isnarrower than that of at least one solid portion of the absorptiongrating.

Embodiment 15. The system according to any of embodiments 9-11, whereina width of at least one slit portion of the absorption grating is widerthan that of at least one solid portion of the absorption grating.

Embodiment 16. The system according to any of embodiments 9-11, whereina width of each slit portion of the absorption grating is narrower thanthat of at least one solid portion of the absorption grating.

Embodiment 17. The system according to any of embodiments 9-11, whereina width of each slit portion of the absorption grating is wider thanthat of at least one solid portion of the absorption grating.

Embodiment 18. The system according to any of embodiments 9-11, whereina width of each slit portion of the absorption grating is narrower thanthat of each solid portion of the absorption grating.

Embodiment 19. The system according to any of embodiments 9-11, whereina width of each slit portion of the absorption grating is wider thanthat of each solid portion of the absorption grating.

Embodiment 20. The system according to any of embodiments 9-11, whereina width of at least one slit portion of the absorption grating isnarrower than that of each solid portion of the absorption grating.

Embodiment 21. The system according to any of embodiments 9-11, whereina width of at least one slit portion of the absorption grating is widerthan that of each solid portion of the absorption grating.

Embodiment 22. The system according to any of embodiments 1-21, whereinthe relative motion between the absorption grating and the filtergrating is in a direction parallel to a front face of the absorptiongrating facing the source.

Embodiment 23. The system according to any of embodiments 1-22, whereinthe absorption grating comprises a metal.

Embodiment 24. The system according to any of embodiments 1-23, whereinthe absorption grating comprises gold.

Embodiment 25. The system according to any of embodiments 1-24, whereina thickness of the absorption grating is 1 mm.

Embodiment 26. The system according to any of embodiments 1-24, whereina thickness of the absorption grating is at least 1 mm.

Embodiment 27. The system according to any of embodiments 1-24, whereina thickness of the absorption grating is no more than 1 mm.

Embodiment 28. The system according to any of embodiments 1-24, whereina thickness of the absorption grating is 0.5 mm.

Embodiment 29. The system according to any of embodiments 1-24, whereina thickness of the absorption grating is at least 0.5 mm.

Embodiment 30. The system according to any of embodiments 1-24, whereina thickness of the absorption grating is no more than 0.5 mm.

Embodiment 31. The system according to any of embodiments 1-30, whereinthe filter grating comprises a first filter material and a second filtermaterial that is less dense than the first filter material.

Embodiment 32. The system according to embodiment 31, wherein the firstfilter material is a metal air and the second filter material is air.

Embodiment 33. The system according to any of embodiments 31-32, whereinthe first filter material is tin.

Embodiment 34. The system according to any of embodiments 31-33, whereinthe filter grating comprises a plurality of strips of the second filtermaterial, with the first filter material disposed alternatingly with theplurality of strips of the second filter material.

Embodiment 35. The system according to any of embodiments 1-34, whereina thickness of the filter grating is 1 mm.

Embodiment 36. The system according to any of embodiments 1-34, whereina thickness of the filter grating is at least 1 mm.

Embodiment 37. The system according to any of embodiments 1-34, whereina thickness of the filter grating is no more than 1 mm.

Embodiment 38. The system according to any of embodiments 1-34, whereina thickness of the filter grating is 0.5 mm.

Embodiment 39. The system according to any of embodiments 1-34, whereina thickness of the filter grating is at least 0.5 mm.

Embodiment 40. The system according to any of embodiments 1-34, whereina thickness of the filter grating is no more than 0.5 mm.

Embodiment 41. The system according to any of embodiments 1-40, whereinthe filter grating moves while the absorption grating stays stationaryduring operation of the source.

Embodiment 42. The system according to any of embodiments 1-40, whereinthe absorption grating moves while the filter grating stays stationaryduring operation of the source.

Embodiment 43. The system according to any of embodiments 1-40, whereinboth the absorption grating and the filter grating move during operationof the source.

Embodiment 44. The system according to any of embodiments 1-43, furthercomprising a motor configured to move at least one of the absorptiongrating and the filter grating relative to the other during operation ofthe source.

Embodiment 45. The system according to embodiment 44, wherein the motoris a piezo-electrical motor.

Embodiment 46. The system according to any of embodiments 1-45, whereinthe absorption grating has a curved geometry.

Embodiment 47. The system according to any of embodiments 1-46, whereinthe filter grating has a curved geometry.

Embodiment 48. The system according to any of embodiments 1-47, whereinthe filter grating is disposed between the source and a patient to beimaged.

Embodiment 49. The system according to any of embodiments 1-48, whereina distance between the filter grating and the source is less than 1meter.

Embodiment 50. The system according to any of embodiments 1-48, whereina distance between the filter grating and the source is less than 500mm.

Embodiment 51. The system according to any of embodiments 1-48, whereina distance between the filter grating and the source is less than 250mm.

Embodiment 52. The system according to any of embodiments 1-51, whereinthe source is an X-ray tube.

Embodiment 53. A method of performing X-ray CT imaging, the methodcomprising:

providing the system according to any of embodiments 1-52 and 94-96;

positioning a patient or sample to be imaged between the filter gratingand the detector;

operating the source to provide X-ray radiation; and

moving at least one of the filter grating and the absorption gratingrelative to the other during operation of the source.

Embodiment 54. The method according to embodiment 53, wherein the filtergrating moves while the absorption grating stays stationary duringoperation of the source.

Embodiment 55. The method according to embodiment 53, wherein theabsorption grating moves while the filter grating stays stationaryduring operation of the source.

Embodiment 56. The method according to embodiment 53, wherein both theabsorption grating and the filter grating move during operation of thesource.

Embodiment 57. The method according to any of embodiments 53-56, whereinthe source is a kVp-switching X-ray source, and wherein an oscillationperiod of the relative movement between the gratings is equal to half atime interval between two adjacent X-ray projections of the source.

Embodiment 58. The method according to any of embodiments 53-56, whereinthe source is a single-kVp X-ray source, and wherein the relativemovement of the gratings is an oscillation movement (relative to eachother) that is optimized for the single-kVp X-ray source.

Embodiment 59. The method according to any of embodiments 53-58, whereinthe patient is a mammal.

Embodiment 60. The method according to any of embodiments 53-59, whereinthe patient is a human.

Embodiment 61. A system for performing X-ray computed tomography (CT)imaging, the system comprising:

a single-kVp X-ray source (non-kVp-switching X-ray source);

a detector for detecting X-ray radiation from the source; and

a filter grating disposed between the source and the detector (to modifythe original X-ray energy spectrum of the X-ray radiation of the X-raysource into two or more spectra), wherein the filter grating ispositioned closer to the source than the detector is,

wherein the system excludes an absorption grating, and

wherein the filter grating is configured to be stationary duringoperation of the source.

Embodiment 62. The system according to embodiment 61, wherein the filtergrating comprises at least two different types of filter material.

Embodiment 63. The system according to any of embodiments 61-62, whereinthe filter grating comprises exactly two different types of filtermaterial.

Embodiment 64. The system according to any of embodiments 61-63, whereinthe filter grating comprises at least two filter strips.

Embodiment 65. The system according to any of embodiments 61-63, whereinthe filter grating comprises exactly two filter strips.

Embodiment 66. The system according to embodiment 65, wherein the twofilter strips comprise a first filter strip of a first filter materialand a second filter strip of a second filter material different from thefirst filter material.

Embodiment 67. The system according to embodiment 66, wherein the firstfilter material is a metal air and the second filter material is air.

Embodiment 68. The system according to any of embodiments 66-67, whereinthe first filter material is tin.

Embodiment 69. The system according to any of embodiments 61-64, whereinthe filter grating comprises a first filter material and a second filtermaterial that is less dense than the first filter material.

Embodiment 70. The system according to embodiment 69, wherein firstfilter material is a metal and the second filter material is air.

Embodiment 71. The system according to any of embodiments 69-70, whereinthe first filter material is tin.

Embodiment 72. The system according to any of embodiments 69-71, whereinthe first and second filter materials are disposed alternatingly in thefilter grating.

Embodiment 73. The system according to any of embodiments 61-72, whereina thickness of the filter grating is 1 mm.

Embodiment 74. The system according to any of embodiments 61-72, whereina thickness of the filter grating is at least 1 mm.

Embodiment 75. The system according to any of embodiments 61-72, whereina thickness of the filter grating is no more than 1 mm.

Embodiment 76. The system according to any of embodiments 61-72, whereina thickness of the filter grating is 0.5 mm.

Embodiment 77. The system according to any of embodiments 61-72, whereina thickness of the filter grating is at least 0.5 mm.

Embodiment 78. The system according to any of embodiments 61-72, whereina thickness of the filter grating is no more than 0.5 mm.

Embodiment 79. The system according to any of embodiments 61-78, whereinthe filter grating has a curved geometry.

Embodiment 80. The system according to any of embodiments 61-79, whereinthe filter grating is disposed between the source and a patient to beimaged.

Embodiment 81. The system according to any of embodiments 61-80, whereina distance between the filter grating and the source is less than 1meter.

Embodiment 82. The system according to any of embodiments 61-80, whereina distance between the filter grating and the source is less than 500mm.

Embodiment 83. The system according to any of embodiments 61-80, whereina distance between the filter grating and the source is less than 250mm.

Embodiment 84. The system according to any of embodiments 61-83, whereinthe source is an X-ray tube.

Embodiment 85. A method of performing X-ray CT imaging, the methodcomprising:

providing the system according to any of embodiments 61-84 and 96;

positioning a patient or sample to be imaged between the filter gratingand the detector; and

operating the source to provide X-ray radiation.

Embodiment 86. The method according to embodiment 85, wherein thepatient is a mammal.

Embodiment 87. The method according to any of embodiments 85-86, whereinthe patient is a human.

Embodiment 88. The system according to any of embodiments 1-52 and61-84, further comprising:

a processor; and

a (non-transitory) machine-readable medium (e.g., a computer-readablemedium) in operable communication with both the processor and thedetector and having machine-executable (e.g., computer-executable)instructions (stored thereon) for image reconstruction based on datareceived from the detector.

Embodiment 89. The system according to embodiment 88, wherein the imagereconstruction is based on a non-linear X-ray data generation model.

Embodiment 90. The system according to any of embodiments 88-89, whereinthe image reconstruction comprises non-linear data modeling andcompressed sensing.

Embodiment 91. The method according to any of embodiments 53-60 and85-87, wherein the system further comprises:

a processor; and

a (non-transitory) machine-readable medium (e.g., a computer-readablemedium) in operable communication with both the processor and thedetector and having machine-executable (e.g., computer-executable)instructions (stored thereon) for image reconstruction based on datareceived from the detector, and wherein the method further comprisesperforming the image reconstruction.

Embodiment 92. The method according to embodiment 91, wherein the imagereconstruction is based on a non-linear X-ray data generation model.

Embodiment 93. The method according to any of embodiments 91-92, whereinthe image reconstruction comprises non-linear data modeling andcompressed sensing.

Embodiment 94. The system according to any of embodiments 1-52, and88-90, wherein the absorption grating is disposed between the filtergrating and the source.

Embodiment 95. The system according to any of embodiments 1-52, 61-84,and 88-90, wherein the filter grating is disposed between the absorptiongrating and the source.

Embodiment 96. The system according to any of embodiments 1-52, 61-84,88-90, 94, and 95, wherein the filter grating is positioned closer tothe source than it is to the detector.

A greater understanding of the present invention and of its manyadvantages may be had from the following examples, given by way ofillustration. The following examples are illustrative of some of themethods, applications, embodiments and variants of the presentinvention. They are, of course, not to be considered as limiting theinvention. Numerous changes and modifications can be made with respectto the invention.

Simulation Parameters

Numerical simulations were carried out to evaluate GOLF systems andmethods of embodiments of the subject invention, both for kVp-switchingand non-kVp-switching dual-energy CT systems. Water and bone wereselected as basis materials, and images were reconstructed viaconventional filtered-back-projection without pre- and post-processingsteps. A CT imaging simulation platform was implemented to evaluate theperformance of the proposed filtration methods. In the simulation, 140kVp was set for single-kVp (non-kVp-switching) dual-energy CT, and 80kVp and 140 kVp X-rays were used for kVp-switching dual-energy CTscanning. For both kVp settings, 100,000 photons were generated, andPoisson noise was added into the projections. In the CT geometry, thedistance between the X-ray focal spot and the rotation center was set to500 mm, and the distance between the X-ray focal spot and the flat-paneldetector was set to 900 mm. There were 888 channels in the detectorarray with cell size of 1 mm. The field-of view was set to 320 mm with512×512 pixels and 0.625 mm pixel size. The chest phantom depicted inFIG. 8 was used, in which titanium-material rods were inserted, asindicated by the large (white) dots near the bottom middle of thephantom.

The signal-to-noise ratio (SNR) is defined as

$\begin{matrix}{\frac{\left( {{\overset{\_}{A}}_{blue} - {\overset{\_}{A}}_{red}} \right)}{\sqrt{\sigma_{Ablue}^{2} + \sigma_{Ared}^{2}}},} & (6)\end{matrix}$

where Ā is the average over a region of interest (ROI), and σ is thestandard variation in the ROI, to quantify a monochromatic image. InFIG. 8, two squares are included in the upper-middle area of thephantom; these boxes are ROIs of 30×30 pixels.

These conditions and parameters were for all numerical simulationexamples.

Example 1

A GOLF_(k) system/method was simulated for kVp-switching baseddual-energy CT. In a CT scan, 1,440 projections were collected wherehalf of the data were at 80 kVp and the other half were at 140 kVp. Thefilter grating used 0.0 mm (air) and 1.0 mm thick tin with a duty cycleof 50%. The thickness of the X-ray absorption grating was 1 mm goldmaterial allowing 99.995% absorption of X-rays at 100 keV. The dutycycle was changed from 10% to 100%, with a duty cycle of 100% beingequivalent to conventional kVp-switching imaging. The monochromaticimages were reconstructed according to Equation 4.

FIG. 9 shows the reconstructed monochromatic images for this example. InFIG. 9, the first row presents images at 100 keV at different absorptiongrating duty cycles, as listed above each column. The first column isfor a duty cycle of 100% (equivalent to conventional kVp-switchingimaging). The second row shows results at 120 keV at differentabsorption grating duty cycles. FIG. 10 shows the local metal areas (theareas around the rods represented by the dots near the lower-middlesection of the phantom) of the images from FIG. 9. The rows and columnsin FIG. 10 are for the same energy/duty cycle combinations as in FIG. 9.FIG. 13A shows the SNR values for the images of FIG. 9. In FIG. 13A, thecross data points are for an energy of 100 keV, the circle data pointsare for an energy of 120 keV, the y-axis shows the SNR, and the x-axisshows the different duty cycles investigated.

Referring to FIGS. 9 and 10, the first column for each shows theperformance that is equivalent to conventional kVp-switching dual-energyCT. There are clear beam hardening artifacts indicated by the (red)arrow present in each image in the first column of FIG. 9, and this canbe seen more clearly in the enlarged views in the first column of FIG.10. At the same location in the images in the second, third, and fourthcolumns of these figures, significantly less artifacts are present, andthe best performance was for r=30%. Referring to FIG. 13A, with asmaller absorption grating opening, the low- and high-energy X-rayspectra have better separation, leading to better image quality, inparticular in terms of beam-hardening reduction.

Example 2

A GOLF_(c) system/method was simulated for single-kVp-based(non-kVp-switching) dual-energy CT. In a CT scan, 1,440 projections werecollected at 140 kVp. The filter grating used 0.1-mm tin and 1.0-mm tinin the two strip filter, and 0.0-mm tin (air) and 1.0-mm tin with 50%duty cycle in the multi-strip grating. The monochromatic images werereconstructed according to Equation 4.

FIG. 11 shows the reconstructed monochromatic images for this example.In FIG. 11, the first row presents images at 100 keV at differentabsorption grating duty cycles for multi-strip gratings (in the firstthree columns) and for a two-strip grating (in the fourth column), aslisted above each column. The second row shows results at 120 keV. FIG.12 shows the local metal areas (the areas around the rods represented bythe dots near the lower-middle section of the phantom) of the imagesfrom FIG. 11. The rows and columns in FIG. 12 are for the sameenergy/duty cycle combinations as in FIG. 11. FIG. 13B shows the SNRvalues for the images of FIG. 11. In FIG. 13B, the cross data points arefor an energy of 100 keV, the circle data points are for an energy of120 keV, the y-axis shows the SNR, and the x-axis shows the differentduty cycles investigated for the multi-strip gratings (first three markson x-axis) and the two-strip grating (right-most mark on x-axis).

Referring to FIGS. 11 and 12, there are some artifacts in the centralarea of the images with the two-strip grating method (far right columnin each of FIGS. 11 and 12). They were caused by the data interpolationin the sinogram, which can be avoided by advanced algorithms, such asiterative reconstruction schemes (see also reference [24] in theReferences section, which is hereby incorporated herein by reference inits entirety). Overall, the two-strip grating approach has a similarperformance to that of the 50% duty cycle multi-strip grating approach.

Comparing the GOLF_(c) method/system of this example to the GOLF_(k)method/system of Example 1, the kVp-switching method results in betterperformance across the board in terms of beam-hardening reduction andSNR, which is consistent with its improved spectrum separationdemonstrated by comparing FIGS. 5A-5C with FIGS. 7A-7B. Also, with theGOLF_(k) system/method, a smaller absorption grating opening (smallerduty cycle) leads to SNR performance for a given radiation dose to thepatient, but at the same time reduces the X-ray source efficacy.

Example 3

A GOLF_(k) system/method was simulated for kVp-switching baseddual-energy CT, including collecting 360, 720, 1080 projections of eachenergy X-rays in turn. The thickness of the X-ray absorption grating was1 mm gold materials having 99.995% absorption of X-rays at 100 keV. Inthe filter grating, the two filtration materials for 80 kVp and 140 kVpX-rays were air and tin, respectively. The thickness of tin material wasset to 0 mm, 0.25 mm, and 0.5 mm in different experiments. The vibrationfrequency of the filter grating was set to match the switching frequencyof X-ray energies in the X-ray source.

FIG. 14 shows the reconstructed monochromatic images. The first columnpresents images at energies of 60 keV, 80 keV and 100 keV (in the first,second, and third rows, respectively) with 0.5 mm tin and 0.5 mm tin(i.e., a conventional kVp-switching method). The right-most columns showthe results for air and 0.5 mm tin (middle column) and air and 1 mm tin(right-most column). FIG. 15 shows a plot of SNR for these images. Thecross data points are for the conventional kVp-switching method, thecircle data points are for the air/1 mm tin GOLF_(k) system/method, andthe star data points are for the air/0.5 mm tin GOLF_(k) system/method.The upper-most (green) line shows connects the star data points, themiddle-most (red) line connects the circle data points, and thelower-most (blue) line connects the cross data points.

Referring to FIGS. 14 and 15, it can be plainly seen that the GOLFksystem/method leads to much clearer monochromatic images, both visuallyand quantitatively. The air/0.5 mm tin GOLF_(k) system/method providesbetter results than the air/1 mm tin GOLF_(k) system/method.

Example 4

A GOLF_(k) system/method was simulated for kVp-switching baseddual-energy CT, including collecting 360, 720, 1080 projections of eachenergy X-rays in turn. The fixed filtration materials were air for 80kVp X-rays and 0.5 mm tin for 140 kVp X-rays. The distance between focalspots was determined by the geometry of the CT scanner and the angulardifference between neighboring projections. In the 360 projectionsetting, a uniform angular sampling around the circular trajectory wasassumed, and the distance between neighboring 80 kVp and 140 kVp X-rayswas 4.36 mm. In the X-ray source, the X-ray focal spots andcorresponding filters were set to a distance of 4.36 mm accordingly tohave the collected neighboring 80 kVp and 140 kVp projection pairs withthe same projection angles. Results were obtained using the X-flyingfocal spot method.

FIG. 16 shows a comparison of the 100 keV, 720-projection 0/0.5 mm Snimage from FIG. 14 for Example 3 (the bottom-middle image in FIG. 14)with the image obtained in this example at 100 keV, 720-projection. Thefirst row shows the images, and the second row shows the error map; thefirst column is the image from Example 3, and the second column is theimage from this example. FIG. 17 shows the images from this exampleacross the top; images left to right are for 360, 720, and 1080projections (100 keV, 0/0.5 mm Sn), respectively, and the plot at thelower portion of FIG. 17 shows a plot of the SNR vs. projection number.The circle data points are for this example (the three images at the topportion of FIG. 17) and are connected by the upper (red) line, and thecross data points are for Example 3 and are connected by the lower(blue) line. The cross data points are for 100 keV, 0/0.5 Sn at thethree different numbers of projections. Referring to FIGS. 16 and 17, itcan be seen that a higher number of projections gives a bettermonochromatic image, and the X-flying focal spot method improves theresults slightly.

Example 5

A GOLF system/method was simulated for K-edge filtering. The top portionof FIG. 18 shows plots of normalized spectra versus X-ray energy for tinand gold (top left, with the (blue) line that is higher at the left ofthe plot being for tin and the (red) line that is higher at the right ofthe plot being for gold) and for tin and gadolinium (top right, with the(blue) line that is higher at the left of the plot being for tin and the(red) line that is higher at the right of the plot being forgadolinium). The bottom portion of FIG. 18 shows plots of spectra versusX-ray energy for without GOLF (“original”) and then using a 0.05 mm tinabsorption grating (bottom left, with the (blue) line that is higher atthe left of the plot being for the original and the (red) line that islower at the left of the plot being for 0.5 mm tin) and for original and0.1 mm gadolinium (bottom right, with the (blue) line that is higher atthe left of the plot being for the original and the (red) line that islower at the left of the plot being for 0.1 mm gadolinium). It should beunderstood that the examples and embodiments described herein are forillustrative purposes only and that various modifications or changes inlight thereof will be suggested to persons skilled in the art and are tobe included within the spirit and purview of this application.

All patents, patent applications, provisional applications, andpublications referred to or cited herein (including those in the“References” section) are incorporated by reference in their entirety,including all figures and tables, to the extent they are notinconsistent with the explicit teachings of this specification.

REFERENCES

-   [1] W. A. Kalender, “X-ray computed tomography,” Physics in medicine    and biology, vol. 51, p. R29, 2006.-   [2] G. Wang, H. Yu, and B. De Man, “An outlook on x-ray CT research    and development,” Medical physics, vol. 35, pp. 1051-1064, 2008.-   [3] G. Wang, T.-H. Lin, P.-c. Cheng, and D. M. Shinozaki, “A general    cone-beam reconstruction algorithm,” Medical Imaging, IEEE    Transactions on, vol. 12, pp. 486-496, 1993.-   [4] K. Taguchi and H. Aradate, “Algorithm for image reconstruction    in multi-slice helical CT,” Medical Physics, vol. 25, pp. 550-561,    1998.-   [5] G. Wang, C. R. Crawford, and W. A. Kalender, “Guest    editorial-Multirow detector and cone-beam spiral/helical CT,”    Medical Imaging, IEEE Transactions on, vol. 19, pp. 817-821, 2000.-   [6] T. R. Johnson, B. Krauss, M. Sedlmair, M. Grasruck, H.    Bruder, D. Morhard, et al., “Material differentiation by dual energy    CT: initial experience,” European radiology, vol. 17, pp. 1510-1517,    2007.-   [7] A. Graser, T. R. Johnson, H. Chandarana, and M. Macari, “Dual    energy CT: preliminary observations and potential clinical    applications in the abdomen,” European radiology, vol. 19, pp.    13-23, 2009.-   [8] L. Yu, S. Leng, and C. H. Mccollough, “Dual-energy CT-based    monochromatic imaging,” Ajr American Journal of Roentgenology, vol.    199, pp. S9-S15, 2012.-   [9] M. Karcaaltincaba and A. Aktaş, “Dual-energy CT revisited with    multidetector CT: review of principles and clinical applications,”    Diagnostic & Interventional Radiology, vol. 17, pp. 181-94, 2010.-   [10] J. Schlomka, E. Roessl, R. Dorscheid, S. Dill, G. Martens, T.    Istel, et al., “Experimental feasibility of multi-energy    photon-counting K-edge imaging in pre-clinical computed tomography,”    Physics in medicine and biology, vol. 53, p. 4031, 2008.-   [11] W. C. Barber, E. Nygard, J. S. Iwanczyk, M. Zhang, E. C.    Frey, B. M. Tsui, et al., “Characterization of a novel photon    counting detector for clinical CT: count rate, energy resolution,    and noise performance,” in SPIE Medical Imaging, 2009, pp.    725824-725824-9.-   [12] H. Gao, H. Yu, S. Osher, and G. Wang, “Multi-energy CT based on    a prior rank, intensity and sparsity model (PRISM),” Inverse    problems, vol. 27, p. 115012, 2011.-   [13] J. Fornaro, S. Leschka, D. Hibbeln, A. Butler, N. Anderson, G.    Pache, et al., “Dual- and multienergy CT: approach to functional    imaging,” Insights Into Imaging, vol. 2, pp. 149-159, 2011.-   [14] B. Li, G. Yadava, and J. Hsieh, “Quantification of head and    body CTDIVOL of dual-energy x-ray CT with fast-kVp switching,”    Medical Physics, vol. 38, pp. 2595-601, 2011.-   [15] R. Carmi, G. Naveh, and A. Altman, “Material separation with    dual-layer CT,” IEEE Nuclear Science Symposium Conference Record    Nuclear Science Symposium, vol. 4, 2005.-   [16] T. G. Flohr, C. H. Mccollough, H. Bruder, M. Petersilka, K.    Gruber, C. Suβ, et al., “et al. First performance evaluation of a    dualsource CT (DSCT) system,” European Radiology, vol. 16, pp.    256-68, 2006.-   [17] M. Petersilka, H. Bruder, B. Krauss, K. Stierstorfer, and T. G.    Flohr, “Technical principles of dual source CT,” European Journal of    Radiology, vol. 68, pp. 362-368, 2008.-   [18] M. Grasruck, S. Kappler, M. Reinwand, and K. Stierstorfer,    “Dual energy with dual source CT and kVp switching with single    source CT: A comparison of dual energy performance,” Proceedings of    SPIE—The International Society for Optical Engineering, vol. 7258,    2009.-   [19] T. G. Flohr, K. Stierstorfer, S. Ulzheimer, H. Bruder, A. N.    Primak, and C. H. Mccollough, “Image reconstruction and image    quality evaluation for a 64-slice CT scanner with z-flying focal    spot,” Medical Physics, vol. 32, pp. 2536-47, 2005.-   [20] G. Wang, “X-ray micro-CT with a displaced detector array,”    Medical Physics, vol. 29, pp. 1634-6, 2002.-   [21] V. Liu, N. R. Lariviere, and G. Wang, “X-ray micro-CT with a    displaced detector array: application to helical cone-beam    reconstruction,” Medical Physics, vol. 30, pp. 2758-61, 2003.-   [22] Q. Yang, W. Cong, Y. Xi, and G. Wang, “Spectral X-ray CT    Reconstruction with Combination of Energy-integrating and    Photon-counting Modules,” Plos ONE, 2016.-   [23] L. Yu, J. A. Christner, S. Leng, J. Wang, J. G. Fletcher,    and C. H. Mccollough, “Virtual monochromatic imaging in dual-source    dual-energy CT: Radiation dose and image quality,” Medical Physics,    vol. 38, pp. 6371-9, 2011.-   [24] M. Beister, D. Kolditz, and W. A. Kalender, “Iterative    reconstruction methods in X-ray CT,” Physica Medica, vol. 28, pp.    94-108, 2012.-   [25] M. J. Kang, C. M. Park, C. H. Lee, J. M. Goo, and H. J. Lee,    “Dual-energy CT: clinical applications in various pulmonary    diseases,” Radiographics, vol. 30, pp. 685-98, 2010.-   [26] Wang et al., International Patent Application Publication No.    WO2016/106348.-   [27] Wang et al., U.S. Patent Application Publication No.    2015/0157286.-   [28] Wang et al., U.S. Patent Application Publication No.    2015/0170361.-   [29] Wang et al., U.S. Patent Application Publication No.    2015/0193927.-   [30] Wang et al., International Patent Application Publication No.    WO2015/164405.-   [31] Wang et al., U.S. Patent Application Publication No.    2016/0113602.-   [32] Wang et al., U.S. Patent Application Publication No.    2016/0135769.-   [33] Wang et al., U.S. Patent Application Publication No.    2016/0166852.-   [34] Wang et al., International Patent Application Publication No.    WO2016/106348.-   [35] Wang et al., International Patent Application Publication No.    WO2016/118960.-   [36] Wang et al., International Patent Application Publication No.    WO2016/154136.-   [37] Wang et al., International Patent Application Publication No.    WO2016/197127.-   [38] Wang et al., International Patent Application Publication No.    WO2017/015381.-   [39] Wang et al., International Patent Application Publication No.    WO2017/019782.-   [40] Wang et al., International Patent Application No.    PCT/US2016/051755.-   [41] Wang et al., International Patent Application NO.    PCT/US2016/061890.-   [42] Wang et al., International Patent Application NO.    PCT/US2017/018456.

What is claimed is:
 1. A system for performing X-ray computed tomography(CT) imaging, the system comprising: an X-ray source; a detector fordetecting X-ray radiation from the source; a filter grating disposedbetween the source and the detector to modify an X-ray energy spectrumof the X-ray radiation into two or more spectra, wherein the filtergrating is positioned closer to the source than the detector is; and anabsorption grating aligned with the filter grating to selectively blockat least a portion of the X-ray radiation, wherein at least one of theabsorption grating and the filter grating is configured to move relativeto the other during operation of the source.
 2. The system according toclaim 1, wherein the source is a kVp-switching X-ray source.
 3. Thesystem according to claim 2, wherein the absorption grating and thefilter grating oscillate relative one another, and the oscillation issynchronized with a switching frequency of the source, such that eachtime the source switches its voltage level, at least one of theabsorption grating and the filter grating moves relative to the other.4. The system according to any of claims 2-3, wherein an oscillationperiod of the relative movement between the gratings is equal to half atime interval between two adjacent X-ray projections of the source. 5.The system according to claim 1, wherein the source is a single-kVpX-ray source.
 6. The system according to claim 5, wherein the relativemovement of the gratings is an oscillation movement relative to eachother that is optimized for the single-kVp X-ray source.
 7. The systemaccording to any of claims 1-6, wherein the filter grating comprises atleast two different types of filter material.
 8. The system according toany of claims 1-7, wherein the absorption grating comprises slitportions and solid portions disposed alternatingly.
 9. The systemaccording to claim 8, wherein a width of each slit portion of theabsorption grating is the same as that of each other slit portion of theabsorption grating.
 10. The system according to claim 8, wherein a widthof at least one slit portion of the absorption grating is narrower thanthat of each solid portion of the absorption grating.
 11. The systemaccording to any of claims 1-10, wherein the relative motion between theabsorption grating and the filter grating is in a direction parallel toa front face of the absorption grating facing the source.
 12. The systemaccording to any of claims 1-11, wherein the absorption gratingcomprises a metal.
 13. The system according to any of claims 1-12,wherein the absorption grating comprises gold.
 14. The system accordingto any of claims 1-13, wherein a thickness of the absorption grating isat least 1 mm.
 15. The system according to any of claims 1-13, wherein athickness of the absorption grating is no more than 1 mm.
 16. The systemaccording to any of claims 1-15, wherein the filter grating comprises aplurality of strips of a first filter material, with a second filtermaterial disposed alternatingly with the plurality of strips of thefirst filter material.
 17. The system according to claim 16, wherein thefirst filter material is a metal and the second filter material is air.18. The system according to any of claims 16-17, wherein the firstfilter material is tin.
 19. The system according to any of claims 1-18,wherein a thickness of the filter grating is no more than 1 mm.
 20. Thesystem according to any of claims 1-18, wherein a thickness of thefilter grating is no more than 0.5 mm.
 21. The system according to anyof claims 1-20, wherein the filter grating moves while the absorptiongrating stays stationary during operation of the source.
 22. The systemaccording to any of claims 1-21, further comprising a motor configuredto move at least one of the absorption grating and the filter gratingrelative to the other during operation of the source.
 23. The systemaccording to claim 22, wherein the motor is a piezo-electrical motor.24. The system according to any of claims 1-23, wherein the absorptiongrating has a curved geometry.
 25. The system according to any of claims1-24, wherein the filter grating has a curved geometry.
 26. The systemaccording to any of claims 1-25, wherein the filter grating is disposedbetween the source and a patient to be imaged.
 27. The system accordingto any of claims 1-26, wherein a distance between the filter grating andthe source is less than 1 meter.
 28. The system according to any ofclaims 1-27, further comprising: a processor; and a machine-readablemedium in operable communication with both the processor and thedetector and having machine-executable instructions for imagereconstruction based on data received from the detector.
 29. A method ofperforming X-ray CT imaging, the method comprising: providing the systemaccording to any of claims 1-28; positioning a patient or sample to beimaged between the filter grating and the detector; operating the sourceto provide X-ray radiation; and moving at least one of the filtergrating and the absorption grating relative to the other duringoperation of the source.
 30. The method according to claim 29, whereinthe filter grating moves while the absorption grating stays stationaryduring operation of the source.
 31. The method according to any ofclaims 29-30, wherein the source is a kVp-switching X-ray source, andwherein an oscillation period of the relative movement between thegratings is equal to half a time interval between two adjacent X-rayprojections of the source.
 32. The method according to any of claims29-30, wherein the source is a single-kVp X-ray source, and wherein therelative movement of the gratings is an oscillation movement (relativeto each other) that is optimized for the single-kVp X-ray source. 33.The method according to any of claims 29-32, wherein the system furthercomprises: a processor; and a machine-readable medium in operablecommunication with both the processor and the detector and havingmachine-executable instructions for image reconstruction based on datareceived from the detector, and wherein the method further comprisesperforming the image reconstruction.
 34. The method according to any ofclaims 29-33, wherein the patient is a human.
 35. A system forperforming X-ray computed tomography (CT) imaging, the systemcomprising: a single-kVp X-ray source; a detector for detecting X-rayradiation from the source; and a filter grating disposed between thesource and the detector, wherein the filter grating is positioned closerto the source than it is to the detector, wherein the system excludes anabsorption grating, and wherein the filter grating is configured to bestationary during operation of the source.
 36. The system according toclaim 35, wherein the filter grating comprises at least two differenttypes of filter material.
 37. The system according to any of claims35-36, wherein the filter grating comprises exactly two filter strips.38. The system according to claim 37, wherein the two filter stripscomprise a first filter strip of a first filter material and a secondfilter strip of a second filter material different from the first filtermaterial.
 39. The system according to claim 38, wherein the first filtermaterial is a metal and the second filter material is air.
 40. Thesystem according to any of claims 38-39, wherein the second filtermaterial is tin.
 41. The system according to any of claims 35-37,wherein the filter grating comprises a first filter material and asecond filter material that is less dense than the first filtermaterial.
 42. The system according to claim 41, wherein first filtermaterial is a metal and the second filter material is air.
 43. Thesystem according to any of claims 41-42, wherein the first filtermaterial is tin.
 44. The system according to any of claims 41-43,wherein the first and second filter materials are disposed alternatinglyin the filter grating.
 45. The system according to any of claims 35-44,wherein a thickness of the filter grating is no more than 1 mm.
 46. Thesystem according to any of claims 35-44, wherein a thickness of thefilter grating is no more than 0.5 mm.
 47. The system according to anyof claims 35-46, wherein the filter grating has a curved geometry. 48.The system according to any of claims 35-47, wherein the filter gratingis disposed between the source and a patient to be imaged.
 49. Thesystem according to any of claims 35-48, wherein a distance between thefilter grating and the source is less than 1 meter.
 50. The systemaccording to any of claims 35-49, further comprising: a processor; and amachine-readable medium in operable communication with both theprocessor and the detector and having machine-executable instructionsfor image reconstruction based on data received from the detector. 51.The system according to claim 50, wherein the image reconstruction isbased on a non-linear X-ray data generation model.
 52. The systemaccording to any of claims 50-51, wherein the image reconstructioncomprises non-linear data modeling and compressed sensing.
 53. A methodof performing X-ray CT imaging, the method comprising: providing thesystem according to any of claims 35-52; positioning a patient or sampleto be imaged between the filter grating and the detector; and operatingthe source to provide X-ray radiation.
 54. The method according to claim53, wherein the system further comprises: a processor; and amachine-readable medium in operable communication with both theprocessor and the detector and having machine-executable instructionsfor image reconstruction based on data received from the detector, andwherein the method further comprises performing the imagereconstruction.
 55. The method according to claim 54, wherein the imagereconstruction is based on a non-linear X-ray data generation model. 56.The method according to any of claims 54-55, wherein the imagereconstruction comprises non-linear data modeling and compressedsensing.
 57. The method according to any of claims 53-56, wherein thepatient is a human.